work (one's) way into (something or some place)
1. To twist or contort one's body in order to fit into some snug place or thing. We had to work our way into the narrow crevice to pass through to the other side. I worked my way into the crawlspace so I could access the electrical wiring.
2. To do the work required to enter into a particular role, job, profession, industry, etc. I decided to change my degree to computer programming so I Could eventually work my way into the video game industry. She's trying to work her way into a management position.